Credit networks represent a way of modeling trust between entities in a
network. Nodes in the network print their own currency and trust each other for
a certain amount of each other's currency. This allows the network to serve as
a decentralized payment infrastructure---arbitrary payments can be routed
through the network by passing IOUs between trusting nodes in their respective
currencies---and obviates the need for a common currency. Nodes can repeatedly
transact with each other and pay for the transaction using trusted currency.
We study the single-sink buy-at-bulk problem with an unknown cost function.
We want to route flow from a set of demand nodes to a root node, where the cost
of routing x total flow along an edge is proportional to f(x) for some concave,
non-decreasing function f satisfying f(0)=0. We present a simple, fast,
deterministic, combinatorial algorithm that takes a set of demands and
constructs a single tree T such that for all f the cost f(T) is a
49.48-approximation of the optimal cost for that f.
We consider the single-source (or single-sink) buy-at-bulk problem with an
unknown concave cost function. We want to route a set of demands along a graph
to or from a designated root node, and the cost of routing x units of flow
along an edge is proportional to some concave, non-decreasing function f such
that f(0) = 0. We present a polynomial time algorithm that finds a distribution
over trees such that the expected cost of a tree for any f is within an
O(1)-factor of the optimum cost for that f.